A football player runs directly down the field for 35m before turning to the right at and angle of 225 degrees from his original direction and running an additional 15m before getting tackled. What is the distance from the player's original starting point to the where he was tackled?
225 is not right, it is all the way around.
To find the distance from the player's original starting point to where he was tackled, we can use the concept of vectors.
First, let's break down the player's movement into its horizontal and vertical components. The player ran directly down the field for 35m, which means he covered only the vertical distance. Therefore, his vertical component of displacement is -35m (negative because he is moving downwards).
Next, the player turns to the right at an angle of 225 degrees from his original direction and runs an additional 15m. This creates a right-angled triangle where the hypotenuse represents the player's overall displacement.
To find the horizontal and vertical components of the player's displacement after turning, we can use trigonometry. The horizontal component can be found using: horizontal displacement = 15m * cos(angle of turn).
In this case, the angle of turn is 225 degrees, so the horizontal displacement would be: horizontal displacement = 15m * cos(225°).
Similarly, the vertical component can be found using: vertical displacement = 15m * sin(angle of turn).
In this case, the angle of turn is 225 degrees, so the vertical displacement would be: vertical displacement = 15m * sin(225°).
Now that we have both the horizontal and vertical displacements, we can use the Pythagorean theorem to find the overall displacement. The formula is: displacement = √(horizontal displacement^2 + vertical displacement^2).
Plugging in the values we calculated, the equation becomes: displacement = √((15m * cos(225°))^2 + (15m * sin(225°))^2).
Evaluating this equation will give us the overall displacement of the player. To find the distance from the player's original starting point to where he was tackled, we take the absolute value of the displacement because distance cannot be negative.
Therefore, calculating the equation will give us the final answer.